A physical energy of the dimension of length that can be formula cut of `c,G` and `(e^(2))/(4 pi epsilon_(0))` is [`c` is velocity of light `G` is universal constant of gravilation e is change

Options

A. `c^2 [G (e^1)/(4 pi epsilon_0)]^(1//2)`
B. `1/(c^2) [(e^2)/(G 4 pi epsilon_0)]^(1//2)`
C. `1/(c^2) G (e^2)/(4 pi epsilon_0)`
D. `1/(c^2) [G (e^2)/(4 pi epsilon_0)]^(1//2)`

Answer

D

Explanation

`L = [c]^a [G]^b [(c^2)/(4pi epsilon_0)]^c`
`[LT^(-1)]^a [M^(-1)L^3 L^(-2)]^b [ML^3 T^(-2)]^c`
`{:(a + 3b + 3c = 1, -a - 2b - 2c = 0, - b + c = 0),(b = 1/2, c = 1/2, darr):}`
`a = -2`
`L = c^(-2) G^(1//2) [(e^2)/(4pi epsilon_0)]^(1//2)`
`L = 1/c^2 [G (e^2)/(4pi epsilon_0)]^(1//2)`